Lightning is build around OOPs concepts.
Wiki for Object-oriented_programming
I was facing with same problem, I had some utility code which was getting repeated in my all components. In Agularjs for given problem we use services. You put your shared code there and simply all component can access your code.
In lightning we have helper you put your code there and all functions in controller within component can access that code. Problem it can't be access by other component.
If you are having strong oops background or coming with java background you know it's best practice to have base class called as BaseEntity (an abstract class) and all your other classes will extend this base class. This base class normally contains properties/methods which will be used in other class (e.g Id field)
So how this will solve your problem.
Create an abstract lightning component you may call it as BaseCmp.
(as you know you can't directly utilize abstract components/classes)
for more refer to
So your basecmp will look like this
<aura:component abstract="true" extensible="true">
<aura:attribute name="yourCommonAttribute" type="String" />
put your all static resources here if you think all components will require it.
Now coming to utility function part, write your all utility class in helper method. All components extending base cmp will get access to utility helper methods/ static resources. You can directly call all basecmp helper methods from your extended cmp. Don't write any controller method here as Lightning Components Developer Guide says:
We don't recommend using inheritance of client-side controllers as this feature may be deprecated in the future to preserve better component encapsulation. We recommend that you put common code in a helper instead.
Best part - your extended component can override these utility functions :)
May be for all - this is not the best solution. But I guess it's cleaner solution to given problem.